Re: [sage-support] Re: Quaternions, how to speed up computation
Thanks. This answer my question and I put the tip
in https://groups.google.com/d/msg/sage-support/NFtI5XqjQWg/sz5WPcFMAgAJ
On Monday, November 19, 2018 at 3:58:50 AM UTC-8, John Cremona wrote:
>
> I recommend importing anything you need from sage.all since the details of
> where everything is might change in time. This works perfectly well:
>
> $ sage -python # so we use Sage's python not my system-wide one
> Python 2.7.15 (default, Nov 2 2018, 14:32:42)
> [GCC 4.8.5 20150623 (Red Hat 4.8.5-28)] on linux2
> Type "help", "copyright", "credits" or "license" for more information.
> >>> from sage.all import PolynomialRing, QQ
> >>> R = PolynomialRing(QQ,'x')
> >>> x = R.gen()
> >>> f = x^3+1 # no good as no preparser
> Traceback (most recent call last):
> File "", line 1, in
> File "sage/structure/element.pyx", line 944, in
> sage.structure.element.Element.__xor__
> (build/cythonized/sage/structure/element.c:9006)
> RuntimeError: Use ** for exponentiation, not '^', which means xor
> in Python, and has the wrong precedence.
>
> # Now we can work with this:
>
> >>> f = x**3+1 # that's better
> >>> f.factor()
> (x + 1) * (x^2 - x + 1)
>
> Another thing I do is to put my commands into a .py file and run pyflakes
> on it, as that reveals what things need to be imported. Then import them
> all from sage.all.
>
> John Cremona
>
> On Mon, 19 Nov 2018 at 11:48, Kolen Cheung > wrote:
>
>> Thank you both for the answers. However, I’m still stuck:
>>
>> Focusing on just translating the first line: R. = QQ[]
>>
>> In sage,
>>
>> >>> preparse("R. = QQ[]")"R = QQ['x']; (x,) = R._first_ngens(1)">>>
>> >>> import_statements(QQ)# ** Warning **: several names for that object: Q,
>> >>> QQfrom sage.rings.rational_field import Q>>> import_statements(R)from
>> >>> sage.rings.qqbar import QQx
>>
>> Immediately I have a question: how come the import_statements of QQ is ...
>> import Q, and the import statement of R is ... import QQx? In either
>> case the namespace in question is not imported. Does it mean ... import
>> Q as QQ and ... import QQx as R respectively?
>>
>> Then I’ve a problem: In sage, I can import them using these import
>> statements. But when entering these 2 import statements in Python,
>>
>> >>> from sage.rings.rational_field import Q
>> ---
>> ImportError Traceback (most recent call last)
>> in ()
>> > 1 from sage.rings.rational_field import Q
>>
>> /usr/lib/python2.7/site-packages/sage/rings/rational_field.py in ()
>> 62 _long_type = int
>> 63
>> ---> 64 from .rational import Rational
>> 65 from .integer import Integer
>> 66
>>
>> /usr/lib/python2.7/site-packages/sage/rings/rational.pyx in init
>> sage.rings.rational (build/cythonized/sage/rings/rational.c:40976)()
>> 94
>> 95
>> ---> 96 import sage.rings.real_mpfr
>> 97 import sage.rings.real_double
>> 98 from libc.stdint cimport uint64_t
>>
>> /usr/lib/python2.7/site-packages/sage/rings/real_mpfr.pyx in init
>> sage.rings.real_mpfr (build/cythonized/sage/rings/real_mpfr.c:44298)()
>> > 1 r"""
>> 2 Arbitrary Precision Real Numbers
>> 3
>> 4 AUTHORS:
>> 5
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_number.pxd in init
>> sage.libs.mpmath.utils (build/cythonized/sage/libs/mpmath/utils.c:8831)()
>> 4 from .real_mpfr cimport RealNumber
>> 5
>> > 6 cdef class ComplexNumber(sage.structure.element.FieldElement):
>> 7 cdef mpfr_t __re
>> 8 cdef mpfr_t __im
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pxd in init
>> sage.rings.complex_number
>> (build/cythonized/sage/rings/complex_number.c:24212)()
>> 8
>> 9
>> ---> 10 cdef class ComplexDoubleField_class(sage.rings.ring.Field):
>> 11 pass
>> 12
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pyx in init
>> sage.rings.complex_double
>> (build/cythonized/sage/rings/complex_double.c:24230)()
>> 96 from cypari2.convert cimport new_gen_from_double,
>> new_t_COMPLEX_from_double
>> 97
>> ---> 98 from . import complex_number
>> 99
>> 100 from .complex_field import ComplexField
>>
>> ImportError: cannot import name complex_number
>> >>> from sage.rings.qqbar import QQx
>> ---
>> ImportError Traceback (most recent call last)
>> in ()
>> > 1 from sage.rings.qqbar import QQx
>>
>> /usr/lib/python2.7/site-packages/sage/rings/qqbar.py in ()
>> 512 rich_to_bool, richcmp_not_equal,
>> 513 op_EQ, op_NE)
>> --> 514 from sage.rings.real_mpfr import RR
>> 515 from sage.rings.real_mpfi import RealIntervalField, RIF,
>> is_RealIntervalFieldElement, RealIntervalField_class
>> 516 from
Re: [sage-support] Re: Quaternions, how to speed up computation
I wonder why for me the result is
>>> import_statements(QQ)
# ** Warning **: several names for that object: Q, QQ from
sage.rings.rational_field import Q
On Monday, November 19, 2018 at 4:05:55 AM UTC-8, Dima Pasechnik wrote:
On Mon, Nov 19, 2018 at 11:58 AM John Cremona > wrote:
> >
> > I recommend importing anything you need from sage.all since the details
> of where everything is might change in time. This works perfectly well:
> >
> > $ sage -python # so we use Sage's python not my system-wide one
> > Python 2.7.15 (default, Nov 2 2018, 14:32:42)
> > [GCC 4.8.5 20150623 (Red Hat 4.8.5-28)] on linux2
> > Type "help", "copyright", "credits" or "license" for more information.
> > >>> from sage.all import PolynomialRing, QQ
> > >>> R = PolynomialRing(QQ,'x')
> > >>> x = R.gen()
> > >>> f = x^3+1 # no good as no preparser
> > Traceback (most recent call last):
> > File "", line 1, in
> > File "sage/structure/element.pyx", line 944, in
> sage.structure.element.Element.__xor__
> (build/cythonized/sage/structure/element.c:9006)
> > RuntimeError: Use ** for exponentiation, not '^', which means xor
> > in Python, and has the wrong precedence.
> >
> > # Now we can work with this:
> >
> > >>> f = x**3+1 # that's better
> > >>> f.factor()
> > (x + 1) * (x^2 - x + 1)
> >
> > Another thing I do is to put my commands into a .py file and run
> pyflakes on it, as that reveals what things need to be imported. Then
> import them all from sage.all.
>
> you can also find out exactly what you need to import:
>
> sage: import_statements("QQ")
> from sage.rings.rational_field import QQ
>
>
> >
> > John Cremona
> >
> > On Mon, 19 Nov 2018 at 11:48, Kolen Cheung > wrote:
> >>
> >> Thank you both for the answers. However, I’m still stuck:
> >>
> >> Focusing on just translating the first line: R. = QQ[]
> >>
> >> In sage,
> >>
> >> >>> preparse("R. = QQ[]")
> >> "R = QQ['x']; (x,) = R._first_ngens(1)"
> >> >>> import_statements(QQ)
> >> # ** Warning **: several names for that object: Q, QQ
> >> from sage.rings.rational_field import Q
> >> >>> import_statements(R)
> >> from sage.rings.qqbar import QQx
> >>
> >> Immediately I have a question: how come the import_statements of QQ is
> ... import Q, and the import statement of R is ... import QQx? In either
> case the namespace in question is not imported. Does it mean ... import Q
> as QQ and ... import QQx as R respectively?
> >>
> >> Then I’ve a problem: In sage, I can import them using these import
> statements. But when entering these 2 import statements in Python,
> >>
> >> >>> from sage.rings.rational_field import Q
> >>
> ---
> >> ImportError Traceback (most recent call
> last)
> >> in ()
> >> > 1 from sage.rings.rational_field import Q
> >>
> >> /usr/lib/python2.7/site-packages/sage/rings/rational_field.py in
> ()
> >> 62 _long_type = int
> >> 63
> >> ---> 64 from .rational import Rational
> >> 65 from .integer import Integer
> >> 66
> >>
> >> /usr/lib/python2.7/site-packages/sage/rings/rational.pyx in init
> sage.rings.rational (build/cythonized/sage/rings/rational.c:40976)()
> >> 94
> >> 95
> >> ---> 96 import sage.rings.real_mpfr
> >> 97 import sage.rings.real_double
> >> 98 from libc.stdint cimport uint64_t
> >>
> >> /usr/lib/python2.7/site-packages/sage/rings/real_mpfr.pyx in init
> sage.rings.real_mpfr (build/cythonized/sage/rings/real_mpfr.c:44298)()
> >> > 1 r"""
> >> 2 Arbitrary Precision Real Numbers
> >> 3
> >> 4 AUTHORS:
> >> 5
> >>
> >> /usr/lib/python2.7/site-packages/sage/rings/complex_number.pxd in init
> sage.libs.mpmath.utils (build/cythonized/sage/libs/mpmath/utils.c:8831)()
> >> 4 from .real_mpfr cimport RealNumber
> >> 5
> >> > 6 cdef class ComplexNumber(sage.structure.element.FieldElement):
> >> 7 cdef mpfr_t __re
> >> 8 cdef mpfr_t __im
> >>
> >> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pxd in init
> sage.rings.complex_number
> (build/cythonized/sage/rings/complex_number.c:24212)()
> >> 8
> >> 9
> >> ---> 10 cdef class ComplexDoubleField_class(sage.rings.ring.Field):
> >> 11 pass
> >> 12
> >>
> >> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pyx in init
> sage.rings.complex_double
> (build/cythonized/sage/rings/complex_double.c:24230)()
> >> 96 from cypari2.convert cimport new_gen_from_double,
> new_t_COMPLEX_from_double
> >> 97
> >> ---> 98 from . import complex_number
> >> 99
> >> 100 from .complex_field import ComplexField
> >>
> >> ImportError: cannot import name complex_number
> >> >>> from sage.rings.qqbar import QQx
> >>
> ---
> >> ImportError
Re: [sage-support] Re: Quaternions, how to speed up computation
On Mon, Nov 19, 2018 at 11:58 AM John Cremona wrote:
>
> I recommend importing anything you need from sage.all since the details of
> where everything is might change in time. This works perfectly well:
>
> $ sage -python # so we use Sage's python not my system-wide one
> Python 2.7.15 (default, Nov 2 2018, 14:32:42)
> [GCC 4.8.5 20150623 (Red Hat 4.8.5-28)] on linux2
> Type "help", "copyright", "credits" or "license" for more information.
> >>> from sage.all import PolynomialRing, QQ
> >>> R = PolynomialRing(QQ,'x')
> >>> x = R.gen()
> >>> f = x^3+1 # no good as no preparser
> Traceback (most recent call last):
> File "", line 1, in
> File "sage/structure/element.pyx", line 944, in
> sage.structure.element.Element.__xor__
> (build/cythonized/sage/structure/element.c:9006)
> RuntimeError: Use ** for exponentiation, not '^', which means xor
> in Python, and has the wrong precedence.
>
> # Now we can work with this:
>
> >>> f = x**3+1 # that's better
> >>> f.factor()
> (x + 1) * (x^2 - x + 1)
>
> Another thing I do is to put my commands into a .py file and run pyflakes on
> it, as that reveals what things need to be imported. Then import them all
> from sage.all.
you can also find out exactly what you need to import:
sage: import_statements("QQ")
from sage.rings.rational_field import QQ
>
> John Cremona
>
> On Mon, 19 Nov 2018 at 11:48, Kolen Cheung wrote:
>>
>> Thank you both for the answers. However, I’m still stuck:
>>
>> Focusing on just translating the first line: R. = QQ[]
>>
>> In sage,
>>
>> >>> preparse("R. = QQ[]")
>> "R = QQ['x']; (x,) = R._first_ngens(1)"
>> >>> import_statements(QQ)
>> # ** Warning **: several names for that object: Q, QQ
>> from sage.rings.rational_field import Q
>> >>> import_statements(R)
>> from sage.rings.qqbar import QQx
>>
>> Immediately I have a question: how come the import_statements of QQ is ...
>> import Q, and the import statement of R is ... import QQx? In either case
>> the namespace in question is not imported. Does it mean ... import Q as QQ
>> and ... import QQx as R respectively?
>>
>> Then I’ve a problem: In sage, I can import them using these import
>> statements. But when entering these 2 import statements in Python,
>>
>> >>> from sage.rings.rational_field import Q
>> ---
>> ImportError Traceback (most recent call last)
>> in ()
>> > 1 from sage.rings.rational_field import Q
>>
>> /usr/lib/python2.7/site-packages/sage/rings/rational_field.py in ()
>> 62 _long_type = int
>> 63
>> ---> 64 from .rational import Rational
>> 65 from .integer import Integer
>> 66
>>
>> /usr/lib/python2.7/site-packages/sage/rings/rational.pyx in init
>> sage.rings.rational (build/cythonized/sage/rings/rational.c:40976)()
>> 94
>> 95
>> ---> 96 import sage.rings.real_mpfr
>> 97 import sage.rings.real_double
>> 98 from libc.stdint cimport uint64_t
>>
>> /usr/lib/python2.7/site-packages/sage/rings/real_mpfr.pyx in init
>> sage.rings.real_mpfr (build/cythonized/sage/rings/real_mpfr.c:44298)()
>> > 1 r"""
>> 2 Arbitrary Precision Real Numbers
>> 3
>> 4 AUTHORS:
>> 5
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_number.pxd in init
>> sage.libs.mpmath.utils (build/cythonized/sage/libs/mpmath/utils.c:8831)()
>> 4 from .real_mpfr cimport RealNumber
>> 5
>> > 6 cdef class ComplexNumber(sage.structure.element.FieldElement):
>> 7 cdef mpfr_t __re
>> 8 cdef mpfr_t __im
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pxd in init
>> sage.rings.complex_number
>> (build/cythonized/sage/rings/complex_number.c:24212)()
>> 8
>> 9
>> ---> 10 cdef class ComplexDoubleField_class(sage.rings.ring.Field):
>> 11 pass
>> 12
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pyx in init
>> sage.rings.complex_double
>> (build/cythonized/sage/rings/complex_double.c:24230)()
>> 96 from cypari2.convert cimport new_gen_from_double,
>> new_t_COMPLEX_from_double
>> 97
>> ---> 98 from . import complex_number
>> 99
>> 100 from .complex_field import ComplexField
>>
>> ImportError: cannot import name complex_number
>> >>> from sage.rings.qqbar import QQx
>> ---
>> ImportError Traceback (most recent call last)
>> in ()
>> > 1 from sage.rings.qqbar import QQx
>>
>> /usr/lib/python2.7/site-packages/sage/rings/qqbar.py in ()
>> 512 rich_to_bool, richcmp_not_equal,
>> 513 op_EQ, op_NE)
>> --> 514 from sage.rings.real_mpfr import RR
>> 515 from sage.rings.real_mpfi import RealIntervalField, RIF,
>> is_RealIntervalFieldElement, RealIntervalField_class
>> 516 from sage.rings.complex_field import
